Thank you all for your responses. It seems like the voters prefer image 1 to image 2. This is actually in accordance to my own preferences as well.
Image 1 is from Capture One Pro v8
Image 2 is from Lightroom CC 2015
The C1P image was processed using the "Version 2" Fuji profile that they have provided. The LR image was processed using the "Provia" profile.
My personal observation is that LR creates that "Dead color" look, even with the Fuji profiles. This is consistent with what I have observed LR do to files from every other camera I have. The C1P colors on the other hand have more "Pop" and the speculars render quite well, making the image more 3D.
The bigger problem though (And something that some here have pointed out) is that the LR image has that horrid "Watercolor" look. fine detail such as grass seem to be painted on and the roses have lost all detail, turning into a mush. Here are some 100% crops for reference.
The C1P image also seems more flexible when it comes to post processing. It takes deconvolusion sharpening well, whereas the LR file develops some horrible double edges. Right click-> view image for 100%
C1P, sharpened
LR, sharpened
Some color grading later, the C1P image looks lovely.
The only thing going for LR IMO is that their lens correction is better. But this is no big deal, I can do that manually for the C1P image.
For me, the way forward is clear. I will be processing the Fuji images only in C1P. Next step would be to shoot some raw and in camera film simulated JPG images side by side and try to recreate the Fuji color palettes within C1P. If anyone is interested, I can share the settings when I am done.